THE COMPETENCE OF COLLEGE ALGEBRA STUDENTS WHO STUDIED HIGH SCHOOL ALGEBRA

109 Pages·04.581 MB·English

by  BLYTH, MARY ISOBEL

THE COMPETENCE OF COLLEGE ALGEBRA STUDENTS
WHO STUDIED HIGH SCHOOL ALGEBRA
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Mary Isotoel Blyth
A dissertation submitted In partial fulfillment
of the requirements for the degree of
Doctor of Philosophy in the
University of Michigan
1950
Committee in charge:
Professor Raleigh Schorling. Chairman
Professor William D. Baten (Michigan State College)
Professor Paul S* Dwyer
Professor Harlan C. Koch
The author wishes to express thanks to every member
of the doctoral committee. Especial thanks are due to
Professor Raleigh Schorling who directed the work, and to
Professors Paul Dwyer and William Baten who gave help with
the statistical analysis. Sincere thanks are also given
to the many teachers at Michigan State College who helped
in the collection of data.
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TABLE OF CONTENTS
CHAPTER PAGE
I. INTRO DUCTION.............................. . . 1
II. REVIEW OP LITERATURE......................... 4
Objectives ................................ 4
Testing of college students .............. 8
Performance in college mathematics • • • • • 12
III. PROCEDURE................................... 16
Determination and validation of objec­
tives . . . . • • • ................ 16
Construction of the test.................. 20
Testing college students .................. 26
IV. FINDINGS..................................... 30
Test g o o r e s .............................. 30
Final grades.............. 37
Other questions................ 48
V. SUMMARY AND CONCLUSION...................... 64
Summary of procedure.................. 64
Summary of findings.............. 65
Limitations of the study............ 68
Suggestions for further study . ........ 69
BIBLIOGRAPHY.................................. 71
APPENDIX.......................................... 75
iii
LIST OF TABLES
TABLE PAGE
I. Percent of Test Devoted to Each Section of
the Outli ne .............................. 23
II. Test Scores with Percentile Rank for High
School Students.................. 25
III. Scores on Test and Amount of High School
A l g e b r a .................................. 31
TV. Measures of Central Tendency and the Stand­
ard Deviation of the Groups Having Various
Amounts of High School Algebra............ 32
V. Test Scores Compared with Published Norms . . 38
VI. Grades in Mathematics 101 of Those Students
with One Tear of High School Algebra . . . . 39
VTI. Test Scores and Final Grades in Mathematics
100a ....................................... 40
VIII. Test Scores and Final Grades in Mathematics
100c....................................... 40
IX. Test Scores and Final Grades in Mathematics.
1 0 1 ....................................... 41
X. Correlation Coefficient between Test Score
and Grade in Mathematics 101 • • • . . . • • 43
XI. Final Grades in Mathematics 1 0 1 ............ 44
XII • Final Grades in Mathematics 100a.......... 46
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TABLE PAGE
XIII* Correlation between Test Scores and Pinal
Grades in Mathematics 100a................ 48
XIV. Students* Opinions of whether Work in College
Mathematics Is Satisfactory • 49
XV. Test Scores of Students who Received Help on
Most Algebra Assignments.................. 50
XVI. Pinal Grades of Students who Received Help on
Most Algebra Assignments................ . 52
XVII. Amount of Mathematics Students Would Advise a
Younger Brother or Sister to Study in High
School.................................... 55
XVIII. Mean Values of the Measures of Liking the
Study of Algebra in High School, Thinking it
Is Easy in College, and Liking it in College 55
XIX. Linear Correlation Coefficients between Enjoy­
ing the Study of Mathematics 101 and Think­
ing it Is Easy............................. 58
XX. Coefficients of Linear Correlation between
Professed Liking for Algebra in High School
and in College • • • • .......... . . . . 59
XXI. Coefficients of Linear Correlation between the
Pinal Grade in College Algebra and Professed
Liking of College Algebra 61
v
TABLE PAGE
XXII* Percent of Students who Mentioned College
Algebra as the Subject they Thought Would
Be Most Useful or Least Useful to Shed • • 62
vi
LIST OF FIGURES
FIGURE PAG®
1. Percent of Students Haring Various Test Scores
according to Amount of Algebra Studied in High
School .......... 35
2. Percent of Students Receiving Various Grades in
Mathematics 101 who Said they Thought their
Work Was Satisfactory.............. 51
3. Percent of Students Receiving Various Grades in
Mathematics 100b who Said they Thought their
Work Was Satisfactory...................... . 51
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CHAPTER I
INTRO DCJCTION
What effect does previous training in algebra have
when a student takes a first course in algebra at eollege?
The study described in the following pages was undertaken to
throw some light on questions such as this. The group stud­
ied was confined to those students who had had algebra in
high school, and presented it as the prerequisite for the
course in college algebra at Michigan State College in the
fall of 1948. Hence, any conclusions reached here might on­
ly be applicable to random samples of the population which
these students at Michigan State College represent. Some of
the questions which the study tried to clarify are listed
below.
1. Is the competence of college students in algebra,
as evidenced by performance on a test devised to measure the
objectives of the second year of high school algebra, re­
lated to the amount of time the student has studied algebra
in high school?
2. Is there agreement among leading teachers of
mathematics as to the content of the second year course in
algebra in high schools?
3. Do those students who have studied algebra in
high school for four semesters earn higher grades in college
1
2
algebra than those who have studied it for only three?
4. Is there any justification for college mathemat­
ics departments to require a prognostic test before assign­
ing a student to a particular college algebra course?
At least tentative answers to the above questions
were suggested by the data. The study also raised addition­
al questions of interest, some of which are as follows:
5. Is there any correlation between test scores on a
particular test given at the beginning of the term, and the
grades given at the end of the term by various instructors
in college algebra?
6. Do significant differences exist between test
scores or final grades of students enrolled in Engineering
or Science courses and those of students enrolled in other
courses?
7. Do students who say they like algebra earn high
grades in college algebra?
8. Do students who say algebra was their favorite
subject in high school also say it is their favorite subject
in college?
9. Is the test used to measure the objectives of the
second year of high school algebra a reliable test?
These are the principal items of this study. Chapter
II contains a report of the Investigations of others in this
and related fields. A detailed description of the procedure
is found in chapter III; the collection of data and their
analyses are found In chapter rv; and a summary and conclu­
sion are in chapter V.